Why is there only one p-Value for the friedman test although it's a two way design

like already in the title: i was searching for something like the 2 way anova but without the normal distribution requirement. the friedman test allows a two way layout but i only get 1 p-valie. but i want to know the impact of rows and column.

What am I misunderstanding? best regards

[Scott MacKenzie]

What data are you analysing? If the data are ratio-scale measurements, then you should consider using the 2-way parametric anova, even if the normality assumption is not met. There are two main reasons. First, the parametric anova is considered robust to violations in the normality assumption. Second, if you use a Friedman test on ratio-scale data, information is lost. Statistical power in the test is sacrificed.

On the first point, try doing a Google search. Have fun navigating through the arguments on each side!

On the second point, let me give a simple example, since many folks either don't consider this or don't understand the issue. If you have three conditions A, B, and C and measured reponse times of, for example, A=40 seconds, B=39 seconds, and C = 20 seconds, you can resonably observe that "A and B took much longer than C". However, this information is lost when doing a Friedman test, because the data are collapsed into ranks: A=1, B=2, and C=3.

[Jonas]

the data were head turn in degree under two factors: age group (1-4) and stimulus direction (only few, +-30 and +-70). and having fun googling around is difficult, i am missing a website which list many many different test, shows requirements, and sorts them in a way anybody can work with. never found such a website.

[Scott MacKenzie]

OK, so head turn (degrees) is a ratio-scale measurment. You'd probably be just using using the parmetric Anova to analyse the data.

[Jonas]

actually i also used the parametric 2 way anova in the end instead of anova ;) but the original question remained and i was happy with the answer i accepted below. but tahbk you for providing some additional information and helping me a bit more in detail regarding this topic!

Answer 1

[Shashank Gupta]

Hi Jonas,

Friedman test in MATLAB as you pointed out give only one p-value which is associated with the column effect. Friedman effect cannot be used for interactions between the row and column factors. Although there are some workaround for separately finding out the p-values for row and column effect.

Test for column effect :-

p = friedman(x)

Test for row effect :-

% For data matrix with no replication, row effect can simply be done by
% taking transpose.
p = friedman(x');

% If the data matrix has replication then it is slightly complicated, below
% is one such template that can be done.
x = reshape(x, [3 2 3]); % First convert the data into 3 dimension data, with the first dimension representing the replicates
x = permute(x, [1 3 2]); % swapping the other two dimensions
x = reshape(x, [9 2]); % restoring the two-dimensional shape
p = friedman(x, 3);

I hope this helps.

Cheers

[Jonas]

many thanks, i saw this dimension swapping already somewhere, but that was a point in time where i didn't need it yet. Couldn't find it in the aftermath. Thank you very much!